Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion

Magnetic Hopfions are localized magnetic solitons with a non-zero 3D topological charge (Hopf index). Here we present an analytical calculation of the Hopfion gyrovector and show that it does not vanish even in infinite sample. The method is based on concept emergent field. particular case simplest non-trivial toroidal Hopf index |QH|=1 cylindrical dot considered dependencies components sizes calculated. Non-zero important any description hopfion dynamics within collective coordinate Thiele´s approach. This article protected by copyright. All rights reserved.